TY - JOUR

T1 - On asymptotic behavior of the mass of rays

AU - Shioya, Takashi

PY - 1990/2

Y1 - 1990/2

N2 - We consider the measure of the set of all unit vectors tangent to rays emanating from a point p in a finitely connected complete open Riemannian 2-manifold M. If M with one end admits total curvature c(M), then this measure tends to min(2πx(M)-c(M), 2π) as p tends to infinity, where x(M) is the Euler characteristic.

AB - We consider the measure of the set of all unit vectors tangent to rays emanating from a point p in a finitely connected complete open Riemannian 2-manifold M. If M with one end admits total curvature c(M), then this measure tends to min(2πx(M)-c(M), 2π) as p tends to infinity, where x(M) is the Euler characteristic.

KW - Complete open manifolds

KW - Gauss-Bonnet theorem

KW - Geodesies

KW - Rays

KW - Total curvature

UR - http://www.scopus.com/inward/record.url?scp=84968475580&partnerID=8YFLogxK

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U2 - 10.1090/S0002-9939-1990-0986652-X

DO - 10.1090/S0002-9939-1990-0986652-X

M3 - Article

AN - SCOPUS:84968475580

SN - 0002-9939

VL - 108

SP - 495

EP - 505

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -